Coordinate Geometry ||Maths|| Chapter 3 Notes

Coordinate Geometry Class 9 ||Maths|| Chapter 3 Notes

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4.1 Introduction

• Coordinate Geometry is the study of geometry using the coordinate plane.
• Coordinate Plane: A two-dimensional plane divided into four quadrants by two perpendicular lines:
  • X-axis (horizontal line)
  • Y-axis (vertical line)

The point where the X-axis and Y-axis intersect is called the origin (denoted as $O(0,0)$).

4.2 Cartesian System

• The system of representing points using coordinates is called the Cartesian System, named after the mathematician René Descartes.
• Each point in the plane is described using an ordered pair $(x,y)$, where:
  • $x$ is the abscissa (horizontal distance from the Y-axis).
  • $y$ is the ordinate (vertical distance from the X-axis).

Coordinates of a Point:

• A point is represented as $(x,y)$, where:
  • $x$ is the distance from the Y-axis.
  • $y$ is the distance from the X-axis.

Example: The point $(3,4)$ means that the point is 3 units to the right of the Y-axis and 4 units above the X-axis.

4.3 Plotting Points in a Plane

To plot a point in the coordinate plane:

1. Start from the origin $(0,0)$.
2. Move horizontally along the X-axis by the value of the abscissa $x$ (right for positive $x$, left for negative $x$).
3. From this point, move vertically by the value of the ordinate $y$ (up for positive $y$, down for negative $y$).

Example:

• Plot the point $(-2,3)$:
  1. Start at the origin.
  2. Move 2 units to the left along the X-axis (since $x=-2$).
  3. Move 3 units up along the Y-axis (since $y=3$).

4.4 The Quadrants

The Cartesian plane is divided into four quadrants based on the signs of the $x$-coordinate and the $y$-coordinate:

1. First Quadrant: Both $x$ and $y$ are positive $(+,+)$.
2. Second Quadrant: $x$ is negative and $y$ is positive $(-,+)$.
3. Third Quadrant: Both $x$ and $y$ are negative $(-,-)$.
4. Fourth Quadrant: $x$ is positive and $y$ is negative $(+,-)$.

4.5 Summary

• Coordinate Plane: A two-dimensional plane where each point is identified by its coordinates $(x,y)$.
• Origin: The point $(0,0)$ where the X-axis and Y-axis intersect.
• X-axis: The horizontal axis.
• Y-axis: The vertical axis.
• Abscissa: The $x$-coordinate of a point, representing the distance from the Y-axis.
• Ordinate: The $y$-coordinate of a point, representing the distance from the X-axis.
• The Cartesian plane is divided into four quadrants.

Key Points to Remember

1. The origin is always $(0,0)$.
2. Coordinates are written in the form $(x,y)$, where $x$ is the horizontal position and $y$ is the vertical position.
3. Moving along the X-axis changes the $x$-coordinate (abscissa), while moving along the Y-axis changes the $y$-coordinate (ordinate).
4. Depending on the signs of $x$ and $y$, a point lies in one of the four quadrants:
   • First Quadrant: $(+,+)$
   • Second Quadrant: $(-,+)$
   • Third Quadrant: $(-,-)$
   • Fourth Quadrant: $(+,-)$

Practice Problems

1. Plot the following points on a graph paper: $(2,3),(-4,-5),(0,2),(-3,4)$.
2. Identify the quadrant in which the following points lie: $(5,-6),(-2,3),(-4,-1),(7,8)$.
3. Write the coordinates of the points lying on:
• The X-axis.
• The Y-axis.

Important Points to Remember:

• The coordinates determine the position of points in a plane.
• The formulas for distance, section, and midpoint play a crucial role in solving problems related to geometry.
• Quadrants help identify the signs of coordinates and the position of points.

This summary captures the key concepts of Chapter 4 of Class 9 NCERT Coordinate Geometry. For a deeper understanding, refer back to your textbook for examples and exercises.